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Experiments on solid-state materials and atomic quantum gases are increasingly investigating similar concepts in many-body quantum physics. Yet, the flavor of experiments on the gaseous atomic materials is different from that of…
We investigate the stability of few-electron quantum phases in vertically coupled quantum dots under a magnetic field of arbitrary strength and direction. The orbital and spin stability diagrams of realistic devices containing up to five…
This thesis presents a set of studies on atomic systems where quantum effects are particularly relevant. These studies have been developed by applying a variety of tools from many-body physics. First of all, we have studied the prospects…
In the recent years, the thermal Hall transport has risen as an important diagnosis of the physical properties of the elementary excitations in various quantum materials, especially among the Mott insulating systems where the electronic…
Strongly correlated quantum systems in low dimensions often exhibit novel quantum ordering. This ordering is sometimes hidden and can be revealed only by examining new `dual' types of correlations. Such ordering leads to novel collective…
Contrary to common belief, the current emitted by a contact embedded in a two-dimensional electron gas (2DEG) is quantized in the presence of electric and magnetic fields. This observation suggests a simple, clearly defined model for the…
The competition between liquid and solid states of strongly correlated electron systems occurs in a novel way in a strong magnetic field. The fact that certain Landau level filling factors are especially favorable for the formation of…
The study of many body physics has provided a scientific playground of surprise and continuing revolution over the past half century. The serendipitous discovery of new states and properties of matter, phenomena such as superfluidity, the…
The fractional quantum Hall effect in 2D electron gases submitted to large magnetic fields remains one of the most striking phenomena in condensed matter physics. Historically, the first observed signature is a Hall resistance quantized to…
With unusually slow and high-resolution sweeps of magnetic field, strong, ultra-narrow (width down to $100 {\rm \mu T}$) resistance peaks are observed in the regime of breakdown of the quantum Hall effect. The peaks are dependent on the…
Recent successes in manufacturing of atomically thin graphite samples (graphene) have stimulated intense experimental and theoretical activity. The key feature of graphene is the massless Dirac type of low-energy electron excitations. This…
The work investigates enantiomers of chiral organo-metallic particles that exhibit a collective memory effect. Under the influence of magnetic field millions of particles in solution form macroscopic shapes and when dispersed again at zero…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
We investigate the emerging consequences of an applied strong in-plane electric field on a macroscopically large graphene sheet subjected to a perpendicular magnetic field, by determining in exact analytical form various many-body…
Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to novel…
While altermagnetic materials are characterized by a vanishing net magnetic moment, their symmetry in principle allows for the existence of an anomalous Hall effect (AHE). Here we introduce a model with altermagnetism in which the emergence…
The spectrum of charged particles in translation-invariant systems in a magnetic field is characterized by the Landau levels, which play a fundamental role in the thermodynamic and transport properties of solids. The topological nature and…
Inspired by recent experiments by Geim et al. we discuss the classical theory of the Hall effect of a 2 dimensional electron gas in an inhomogeneous magnetic field. The field modulation is in the form of flux tubes created by a…
We are concerned with the global existence of finite energy weak solutions to 3D density-dependent magnetohydrodynamics (MHD) system with Hall-effect set in a general smooth bounded domain. The perfectly conducting wall boundary condition…
A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to…